8,109 research outputs found
Design sensitivity analysis of nonlinear structural response
A unified theory is described of design sensitivity analysis of linear and nonlinear structures for shape, nonshape and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified viewpoint. A general formula for design sensitivity analysis is derived. Simple analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use
Strong inapproximability of the shortest reset word
The \v{C}ern\'y conjecture states that every -state synchronizing
automaton has a reset word of length at most . We study the hardness
of finding short reset words. It is known that the exact version of the
problem, i.e., finding the shortest reset word, is NP-hard and coNP-hard, and
complete for the DP class, and that approximating the length of the shortest
reset word within a factor of is NP-hard [Gerbush and Heeringa,
CIAA'10], even for the binary alphabet [Berlinkov, DLT'13]. We significantly
improve on these results by showing that, for every , it is NP-hard
to approximate the length of the shortest reset word within a factor of
. This is essentially tight since a simple -approximation
algorithm exists.Comment: extended abstract to appear in MFCS 201
On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems
We show improved NP-hardness of approximating Ordering Constraint
Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, Maximum
Acyclic Subgraph and Maximum Betweenness, we prove inapproximability of
and .
An OCSP is said to be approximation resistant if it is hard to approximate
better than taking a uniformly random ordering. We prove that the Maximum
Non-Betweenness Problem is approximation resistant and that there are width-
approximation-resistant OCSPs accepting only a fraction of
assignments. These results provide the first examples of
approximation-resistant OCSPs subject only to P \NP
Accurate determination of electric-dipole matrix elements in K and Rb from Stark shift measurements
Stark shifts of potassium and rubidium D1 lines have been measured with high
precision by Miller et al [1]. In this work, we combine these measurements with
our all-order calculations to determine the values of the electric-dipole
matrix elements for the 4p_j-3d_j' transitions in K and for the 5p_j-4d_j'
transitions in Rb to high precision. The 4p_1/2-3d_3/2 and 5p_1/2-4d_3/2
transitions contribute on the order of 90% to the respective polarizabilities
of the np_1/2 states in K and Rb, and the remaining 10% can be accurately
calculated using the relativistic all-order method. Therefore, the combination
of the experimental data and theoretical calculations allows us to determine
the np-(n-1)d matrix elements and their uncertainties. We compare these values
with our all-order calculations of the np-(n-1)d matrix elements in K and Rb
for a benchmark test of the accuracy of the all-order method for transitions
involving nd states. Such matrix elements are of special interest for many
applications, such as determination of magic wavelengths in alkali-metal atoms
for state-insensitive cooling and trapping and determination of blackbody
radiation shifts in optical frequency standards with ions.Comment: 5 page
Phytochemical investigation of seeds of Trachyspermum ammi Linn. by GC-MS
The present study embraces phytochemical investigation of the essential oil extracted from the mature seeds of Trachyspermum ammi Linn for different constituents by subjecting the oil to gas chromatography-mass spectrometry (GC-MS) analysis. The identification of the constituents is based upon retention indices and by comparison of their mass spectral fragmentation patterns against the commercial library mass spectra (Wiley, Nist etc.). Ellagic acid (EA), which is a natural phenol antioxidant, has been isolated from methanol extract from the mature seeds of Trachyspermum ammi Linn. Also, Thymol (Thl), a naturally occurring phenolic compound, has been crystallized by the reported standard procedure from oil extracted from these mature seeds. Both these compounds have been evaluated for their possible anti-cancer effect against a selected panel of human cancer cell lines by means of sulforhodamine B assay
Phytochemical Study of Nothapodytes foetida by LC-ESI-MS
In the present study, hyphenated technique using dyad system of high performance liquid chromatography with diode array detection directly coupled with electrospray ionization mass spectrometry (LC-ESI-MS) has been employed for identification of camptothecines and some minor constituents of methanol extract from different parts of Nothapodytes foetida on the basis of systematic mass spectrum analysis without isolation and purification of these components. Also, a simple, precise, sensitive and reproducible LC-MS method has been developed for quantification of camptothecin (CPT), a potent cytotoxic isoquinoline alkaloid, in methanol extract from these different parts of Nothapodytes foetida using the same technique
Recovery Ventilation and Oxygen Debt-A Mathematical Model for the Prediction of Recovery Ventilation
A Mathematical model has been evolved for the estimation of recovery ventilation following an exercise. The model has been used to estimate recovery ventilation in moderate to heavy exercise for a period of 32 minutes. The model gives satisfactory predictions for persons of different age groups and under different environment conditions thus establishing its universal applicability
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